Current generation unclear magnetic resonance (NMR) logging tools such as Schlumberger's MR SCANNER™ make multiple measurements in which several acquisition parameters are varied. The parameters are varied to induce changes in the NMR response that are analyzed and interpreted in terms of fluid and/or rock properties. Typically, wait times (WT) and echo spacings (TE) are varied. For all measurements, a train of echoes is measured, which constitutes the raw NMR signal. Analysis of the echo train decays provides distributions of transverse relaxation times, T2. Monitoring the changes in echo train amplitude with different WT allows one to determine the longitudinal relaxation times, T1. Similarly, variations in decay rates and echo train amplitudes with different TE allow us to measure molecular diffusion rates, D.
Provided that enough measurements are acquired with an appropriate range of acquisition parameters, it is possible to perform a simultaneous inversion of all data to derive 3-dimensional distributions in T2-T1-D space. This approach is currently employed in MR SCANNER™ and CMR™ fluid characterization measurement and interpretation. The advantages of using a simultaneous inversion rather than separate evaluation of T2, T1, and D distributions are (i) improvement in precision, and (ii) reduction in number of measurements and therefore total time required to extract the full distributions.
In addition to WT and TE variations, certain NMR logging tools acquire data at different frequencies. The effect of changing frequency is to change the depth of investigation (DOI) of the NMR measurement. For example the MR SCANNER™ tool has volumes of investigation that form thin (˜1-3 mm) area in front of the antenna. The distance of the arc from the antenna face depends on frequency. A lower frequency corresponds to an arc farther from the antenna. Since the tool is run eccentered with the antenna pressed against the borehole wall, a lower frequency implies a deeper depth of investigation.
Two opposing strategies have been adopted for evaluating data acquired at different frequencies (i.e., different DOIs). The first strategy involves combining data from all DOIs and performing a single inversion. This approach is used to improve precision on a single set of answers and is appropriate provided the fluid distribution does not vary over the range of DOIs accessed during the measurements. Combining or averaging data acquired at different frequencies could lead to inconsistent datasets and erroneous interpretation if fluid distributions vary with DOI. Results obtained with MR SCANNER™ have demonstrated that fluid distributions can change substantially over the first few inches from the wellbore into the formation. The fluid variations occur because of the invasion of drilling fluid filtrate into the formation. The invading drilling fluid (filtrate) displaces movable native fluids, both water and hydrocarbon. In view of these observations, a second strategy has been adopted for MR SCANNER™. Sufficient measurements are acquired to allow independent inversion and interpretation at each DOI (i.e., at each frequency). This approach is quite general and correctly accounts for varying fluid distributions. However, it is not optimal for measurement precision. This is particularly important for the deeper DOIs (lower frequency), which typically have poorer signal-to-noise.
Several methods have been proposed to handle inversion of NMR echo decay train suites into distributions. Those methods, however, treat each experiment in a set individually or independently.